Measurement exploratory data analysis

from tabulate import tabulate
from IPython.display import Markdown, HTML
import matplotlib.pylab as plt
from typing import List, Tuple

import pandas as pd
import numpy as np
from scipy.signal import find_peaks
from scipy.signal import butter, lfilter

from tsfel.feature_extraction.features import fundamental_frequency

import os
import sys
sys.path.append('../../')
from feature import mafaulda as src
from feature import discovery as fdiscovery

pd.set_option("display.notebook_repr_html", False)

Define data sources

DIR = '../../air_conditioning/'
file_list = [
    DIR + 'excool_digitalis/high_pressure_pump_40percent__1.tsv',
    DIR + 'excool_digitalis/high_pressure_pump_40percent__2.tsv',
    DIR + 'excool_digitalis/high_pressure_pump_40percent_speed_up__3.tsv',
    DIR + 'excool_digitalis/high_pressure_pump_80percent__4.tsv',
    DIR + 'shc2/compressor_shc2_klima4_bad.tsv',
    DIR + 'shc2/compressor_shc2_klima5_good.tsv',
    DIR + 'vertiv_digitalis/compressor_top_1.tsv',
    DIR + 'vertiv_digitalis/compressor_top_2.tsv',
    DIR + 'vertiv_digitalis/compressor_top_3.tsv',
    DIR + 'vertiv_digitalis/compressor_base.tsv',
    DIR + 'vertiv_digitalis/compressor_side.tsv'
]

T_WAVEFORM = 5
T_SEC = T_WAVEFORM
NFFT = 512

DATASET = []

Import dataset

Fs = 1160     # 1160 Hz +/-150 Hz (1020 - 1340 Hz)

for filename in file_list:
    ts = pd.read_csv(filename, delimiter='\t', index_col=False, header=None, names=['x', 'y', 'z'])
    # Calculate amplitude in m/s^2 Beaglebone Black ADC and ADXL335 resolution (VIN 1.8V, 12bits)
    for dim in ts.columns:
        ts[dim] = ts[dim] * (1800 / 4096)  # ADC to mV
        ts[dim] = (ts[dim] / 180) * 9.81  # mV to m/s^2 (180 mV/g)
        ts[dim] -= ts[dim].mean()

    ts['t'] = ts.index * (1 / Fs)
    ts.set_index('t', inplace=True)
    DATASET.append((os.path.basename(filename), ts))

for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    ts.info()
    print()

high_pressure_pump_40percent__1.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 38832 entries, 0.0 to 33.475
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       38832 non-null  float64
 1   y       38832 non-null  float64
 2   z       38832 non-null  float64
dtypes: float64(3)
memory usage: 1.2 MB

high_pressure_pump_40percent__2.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 59014 entries, 0.0 to 50.873275862068965
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       59014 non-null  float64
 1   y       59014 non-null  float64
 2   z       59014 non-null  float64
dtypes: float64(3)
memory usage: 1.8 MB

high_pressure_pump_40percent_speed_up__3.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 37931 entries, 0.0 to 32.69827586206897
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       37931 non-null  float64
 1   y       37931 non-null  float64
 2   z       37931 non-null  float64
dtypes: float64(3)
memory usage: 1.2 MB

high_pressure_pump_80percent__4.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 18550 entries, 0.0 to 15.99051724137931
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       18550 non-null  float64
 1   y       18550 non-null  float64
 2   z       18550 non-null  float64
dtypes: float64(3)
memory usage: 579.7 KB

compressor_shc2_klima4_bad.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 46205 entries, 0.0 to 39.83103448275862
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       46205 non-null  float64
 1   y       46205 non-null  float64
 2   z       46205 non-null  float64
dtypes: float64(3)
memory usage: 1.4 MB

compressor_shc2_klima5_good.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 34394 entries, 0.0 to 29.64913793103448
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       34394 non-null  float64
 1   y       34394 non-null  float64
 2   z       34394 non-null  float64
dtypes: float64(3)
memory usage: 1.0 MB

compressor_top_1.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 21039 entries, 0.0 to 18.136206896551723
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       21039 non-null  float64
 1   y       21039 non-null  float64
 2   z       21039 non-null  float64
dtypes: float64(3)
memory usage: 657.5 KB

compressor_top_2.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 13585 entries, 0.0 to 11.710344827586207
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       13585 non-null  float64
 1   y       13585 non-null  float64
 2   z       13585 non-null  float64
dtypes: float64(3)
memory usage: 424.5 KB

compressor_top_3.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 18491 entries, 0.0 to 15.939655172413794
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       18491 non-null  float64
 1   y       18491 non-null  float64
 2   z       18491 non-null  float64
dtypes: float64(3)
memory usage: 577.8 KB

compressor_base.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 13447 entries, 0.0 to 11.591379310344827
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       13447 non-null  float64
 1   y       13447 non-null  float64
 2   z       13447 non-null  float64
dtypes: float64(3)
memory usage: 420.2 KB

compressor_side.tsv

<class 'pandas.core.frame.DataFrame'>
Index: 22793 entries, 0.0 to 19.648275862068964
Data columns (total 3 columns):
 #   Column  Non-Null Count  Dtype  
---  ------  --------------  -----  
 0   x       22793 non-null  float64
 1   y       22793 non-null  float64
 2   z       22793 non-null  float64
dtypes: float64(3)
memory usage: 712.3 KB

for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    display(tabulate(ts.describe(), headers='keys', tablefmt='html'))

high_pressure_pump_40percent__1.tsv

	x	y	z
count	38832	38832	38832
mean	-5.91039e-15	-7.28292e-15	-3.52325e-15
std	0.156233	0.269068	0.088905
min	-1.97741	-1.71713	-0.337432
25%	-0.0853405	-0.184319	-0.0500295
50%	0.0104603	0.00728275	-0.00212907
75%	0.106261	0.174934	0.0457713
max	0.705016	1.10899	0.428974

high_pressure_pump_40percent__2.tsv

	x	y	z
count	59014	59014	59014
mean	-4.19614e-15	4.07935e-15	-8.59432e-15
std	0.0943096	0.197273	0.0690056
min	-0.418335	-0.851503	-0.275299
25%	-0.0590825	-0.132997	-0.0357975
50%	-0.0111821	0.010704	-0.0118473
75%	0.0606685	0.130455	0.0360531
max	0.372021	0.72921	0.251605

high_pressure_pump_40percent_speed_up__3.tsv

	x	y	z
count	37931	37931	37931
mean	4.76105e-15	3.5367e-15	4.15412e-15
std	0.850667	0.407354	0.303165
min	-2.90341	-1.83915	-0.989876
25%	-0.388635	-0.23449	-0.151619
50%	0.0664185	0.00501154	-0.0318681
75%	0.30592	0.244513	0.111833
max	2.50934	1.84918	1.11774

high_pressure_pump_80percent__4.tsv

	x	y	z
count	18550	18550	18550
mean	-2.68742e-15	-2.5005e-15	8.80077e-15
std	0.937496	0.615358	0.370609
min	-2.89281	-2.59842	-1.02679
25%	-0.641493	-0.418954	-0.284332
50%	0.0530623	0.0121494	-0.0208799
75%	0.579967	0.419303	0.242572
max	2.59178	2.38322	1.08083

compressor_shc2_klima4_bad.tsv

	x	y	z
count	46205	46205	46205
mean	2.34361e-16	-2.87923e-15	8.44255e-15
std	0.0839049	0.0752622	0.190291
min	-0.395752	-0.459668	-1.17776
25%	-0.0604496	-0.0285645	-0.123954
50%	-0.0125492	-0.00461432	-0.00420275
75%	0.0593014	0.0432861	0.115548
max	0.394604	0.450439	1.09751

compressor_shc2_klima5_good.tsv

	x	y	z
count	34394	34394	34394
mean	5.22877e-16	3.73079e-15	5.67769e-15
std	0.105077	0.230046	0.392763
min	-0.426641	-0.571587	-1.26612
25%	-0.0673884	-0.164434	-0.236258
50%	0.0044622	0.00321782	0.00324429
75%	0.0523626	0.170869	0.218796
max	0.579267	0.625923	1.2726

compressor_top_1.tsv

	x	y	z
count	21039	21039	21039
mean	-1.39211e-15	1.57009e-15	5.34959e-15
std	1.32462	1.42278	0.39025
min	-3.41267	-3.87311	-0.928501
25%	-0.945797	-1.04699	-0.329746
50%	0.0361615	0.126574	-0.0183938
75%	1.06602	0.964831	0.316909
max	2.86228	3.40775	1.25097

compressor_top_2.tsv

	x	y	z
count	13585	13585	13585
mean	-6.58815e-15	2.22394e-15	1.42161e-15
std	1.35929	1.4691	0.372723
min	-3.63639	-4.11425	-0.88664
25%	-0.953964	-1.07258	-0.311836
50%	0.0519447	0.148884	-0.0244333
75%	1.10575	1.01109	0.286919
max	2.94992	3.54981	1.43653

compressor_top_3.tsv

	x	y	z
count	18491	18491	18491
mean	5.09573e-15	6.55939e-16	-8.19405e-15
std	1.61442	1.31795	0.85044
min	-3.85041	-3.72399	-3.17339
25%	-1.16799	-0.849971	-0.514919
50%	-0.186031	0.155937	0.0119848
75%	1.27493	0.850493	0.490989
max	3.7418	3.00601	2.52676

compressor_base.tsv

	x	y	z
count	13447	13447	13447
mean	-2.2716e-15	-7.28139e-16	4.6156e-15
std	1.30529	2.3902	0.733422
min	-2.49659	-5.04931	-1.68723
25%	-1.15538	-1.95974	-0.513669
50%	0.0181831	0.243679	0.0850858
75%	1.09594	2.09982	0.516189
max	2.62875	4.29126	1.6179

compressor_side.tsv

	x	y	z
count	22793	22793	22793
mean	1.78719e-15	4.33564e-15	-2.57807e-15
std	1.14264	1.66626	1.30827
min	-3.21371	-3.61176	-2.85124
25%	-0.67499	-1.38439	-0.935224
50%	-0.0522853	-0.186877	-0.192768
75%	0.953623	1.32199	0.908941
max	2.31878	4.17206	3.30396

Time domain waveform

axis = ['x', 'y', 'z']
for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    
    ax = ts[axis].plot(figsize=(20, 8), grid=True, subplots=True)
    for i, axname in enumerate(axis):
        ax[i].set_xlabel('Time [s]')
        ax[i].set_ylabel(f'Amplitude ({axname}) [m/s^2]')
    plt.show()               # plt.savefig('waveform.png')

high_pressure_pump_40percent__1.tsv

high_pressure_pump_40percent__2.tsv

high_pressure_pump_40percent_speed_up__3.tsv

high_pressure_pump_80percent__4.tsv

compressor_shc2_klima4_bad.tsv

compressor_shc2_klima5_good.tsv

compressor_top_1.tsv

compressor_top_2.tsv

compressor_top_3.tsv

compressor_base.tsv

compressor_side.tsv

Time domain waveform zoom detail

axis = ['x', 'y', 'z']
for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    ax = (ts[axis].iloc[int(T_WAVEFORM*Fs):int(T_WAVEFORM*Fs)+Fs]
                  .plot(figsize=(20, 10), grid=True, subplots=True))
    
    for i, axname in enumerate(axis):
        ax[i].set_xlabel('Time [s]')
        ax[i].set_ylabel(f'Amplitude ({axname}) [m/s^2]')
        plt.show()      # plt.savefig('waveform_zoom.png')

high_pressure_pump_40percent__1.tsv

high_pressure_pump_40percent__2.tsv

high_pressure_pump_40percent_speed_up__3.tsv

high_pressure_pump_80percent__4.tsv

compressor_shc2_klima4_bad.tsv

compressor_shc2_klima5_good.tsv

compressor_top_1.tsv

compressor_top_2.tsv

compressor_top_3.tsv

compressor_base.tsv

compressor_side.tsv

def spectogram(x):
    fig, ax = plt.subplots(figsize=(15, 4))
    cmap = plt.get_cmap('inferno')
    pxx, freqs, t, im = plt.specgram(
        x, NFFT=NFFT, Fs=Fs,
        detrend='mean',
        mode='magnitude', scale='dB',
        cmap=cmap, vmin=-60
    )
    fig.colorbar(im, aspect=20, pad=0.04)
    ax.set_xlabel('Time [s]')
    ax.set_ylabel('Frequency [Hz]')
    src.resolution_calc(Fs, NFFT)
    return freqs, pxx

def window_idx(t):
    return (Fs * t) // NFFT + 1

def spectrum_slice(freqs, Pxx, t):
    fig, ax = plt.subplots(2, 1, figsize=(20, 8))
    n = window_idx(t)

    dB = 20 * np.log10(Pxx.T[n] / 0.000001)
    ax[0].plot(freqs, dB)      # 1 dB = 1 um/s^2
    ax[0].grid(True)
    ax[0].set_xlabel('Frequency [Hz]')
    ax[0].set_ylabel('Amplitude [dB]')
    
    ax[1].plot(freqs, Pxx.T[n])
    ax[1].grid(True)
    ax[1].set_xlabel('Frequency [Hz]')
    ax[1].set_ylabel('Amplitude [m/s^2]')
    return n


def get_max_frequency(freqs, Pxx, i):
    max_freq = freqs[np.argmax(Pxx.T[i])]
    return max_freq


def get_peaks(freqs, Pxx, i, top=5):
    amplitudes = Pxx.T[i]
    peaks, _ = find_peaks(amplitudes, distance=3)

    fundamental = get_max_frequency(freqs, Pxx, i)
    f_top = freqs[peaks[np.argsort(amplitudes[peaks])]][::-top]
    y_top = np.sort(amplitudes[peaks])[::-top]

    return pd.DataFrame({
        'f': f_top,
        'y': y_top,
        '1x': f_top / fundamental 
    })


def butter_bandpass_filter(data, lowcut, highcut, fs, order=5):
    b, a = butter(order, [lowcut, highcut], fs=fs, btype='band')
    y = lfilter(b, a, data)
    return y


def get_spectrograms(DATASET: List[pd.DataFrame], axis: str) -> list:
    spectrograms = []

    for name, ts in DATASET:
        base_freq = fundamental_frequency(ts[axis], Fs)
        display(Markdown(f'**{name}** *({axis.upper()} axis, Fundamental = {base_freq:.4f} Hz)*'))
        
        freqs, Pxx = spectogram(ts['x'])
        spectrograms.append((name, freqs, Pxx))
        plt.show()          # plt.savefig(f'x_axis_fft_{NFFT}.png')
    
    return spectrograms


def show_spectrogram_detail(spectrograms: list, axis: str, t: float):
    for name, freqs, Pxx in spectrograms:
        display(Markdown(f'**{name}** ({axis.upper()} axis @ {t}s)'))
        i_window = spectrum_slice(freqs, Pxx, t)
        # Incorrect fundamental frequency:
        # print(fdiscovery.harmonic_product_spectrum(freqs, Pxx.T[i_window]))
        plt.show()           #plt.savefig(f'x_axis_fft_{NFFT}_at_{T_SEC}s.png')


def show_mms_peaks(spectrograms: list, axis: str, t: float):
    for name, freqs, Pxx in spectrograms:
        display(Markdown(f'**{name}** ({axis.upper()} axis @ {t}s)'))
    
        i_window = window_idx(t)
        peaks = fdiscovery.mms_peak_finder(Pxx.T[i_window])
        
        fig, ax = plt.subplots(1, 1, figsize=(15, 3))
        ax.grid(True)
        ax.plot(freqs, Pxx.T[i_window])
        ax.scatter(freqs[peaks], Pxx.T[i_window][peaks], marker='^', color='red')
        ax.set_xlabel('Frequency [Hz]')
        
        plt.show()


def show_harmonic_series(spectrograms: list, axis: str, t: float):
    # https://stackoverflow.com/questions/1982770/changing-the-color-of-an-axis
    for name, freqs, Pxx in spectrograms:
        display(Markdown(f'**{name}** ({axis.upper()} axis @ {t}s)'))
    
        i_window = window_idx(t)
        h_series = fdiscovery.harmonic_series_detection(freqs, Pxx.T[i_window], Fs, NFFT)
    
        # Find best (sum of harmonics' amplitudes in the largest)
        max_harmonic_amp_idx = np.argmax([
            sum([h[1] for h in s]) / len(s)
            for s in h_series
        ])
        best_harmonic_series = pd.DataFrame(
            h_series[max_harmonic_amp_idx],
            columns=['Frequency [Hz]', 'Amplitude [m/s^2]']
        )
        best_harmonic_series.index += 1
        display(tabulate(best_harmonic_series, headers='keys', tablefmt='html'))
    
        # Plot found harmonic series
        fig, ax = plt.subplots(1, 8, figsize=(30, 4))
        for i in range(8):
            s = h_series[i+1]
            if i == max_harmonic_amp_idx:
                ax[i].xaxis.label.set_color('red')
    
            ax[i].plot(freqs, Pxx.T[i_window])
            ax[i].scatter([x[0] for x in s], [x[1] for x in s], marker='^', color='red')
            ax[i].set_xlabel('Frequency [Hz]')
    
        plt.show()

def show_spectra_largest_amplitudes(spectrograms: list, axis: str, t: float):
    for name, freqs, Pxx in spectrograms:
        display(Markdown(f'**{name}** ({axis.upper()} axis @ {t}s)'))

        i_window = window_idx(t)
        x_fundamental = get_max_frequency(freqs, Pxx, i_window)
        peaks = get_peaks(freqs, Pxx, i_window)
        
        display(Markdown(f'- *Fundamental frequency:* {x_fundamental} Hz'))
        display(tabulate(peaks.head(5), headers='keys', tablefmt='html'))

Spectrogram in X axis

x_spectra = get_spectrograms(DATASET, 'x')

high_pressure_pump_40percent__1.tsv (X axis, Fundamental = 25.5408 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

high_pressure_pump_40percent__2.tsv (X axis, Fundamental = 25.4943 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

high_pressure_pump_40percent_speed_up__3.tsv (X axis, Fundamental = 47.8300 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

high_pressure_pump_80percent__4.tsv (X axis, Fundamental = 47.5881 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_shc2_klima4_bad.tsv (X axis, Fundamental = 0.0251 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_shc2_klima5_good.tsv (X axis, Fundamental = 28.8702 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_top_1.tsv (X axis, Fundamental = 47.9129 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_top_2.tsv (X axis, Fundamental = 49.4398 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_top_3.tsv (X axis, Fundamental = 48.6810 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_base.tsv (X axis, Fundamental = 48.8258 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_side.tsv (X axis, Fundamental = 49.6205 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

Spectrogram detail in X axis

show_spectrogram_detail(x_spectra, 'x', T_SEC)

high_pressure_pump_40percent__1.tsv (X axis @ 5s)

high_pressure_pump_40percent__2.tsv (X axis @ 5s)

high_pressure_pump_40percent_speed_up__3.tsv (X axis @ 5s)

high_pressure_pump_80percent__4.tsv (X axis @ 5s)

compressor_shc2_klima4_bad.tsv (X axis @ 5s)

compressor_shc2_klima5_good.tsv (X axis @ 5s)

compressor_top_1.tsv (X axis @ 5s)

compressor_top_2.tsv (X axis @ 5s)

compressor_top_3.tsv (X axis @ 5s)

compressor_base.tsv (X axis @ 5s)

compressor_side.tsv (X axis @ 5s)

Peaks in frequency spectrum in X axis

• MMS peak finder algorithm

show_mms_peaks(x_spectra, 'x', T_SEC)

high_pressure_pump_40percent__1.tsv (X axis @ 5s)

high_pressure_pump_40percent__2.tsv (X axis @ 5s)

high_pressure_pump_40percent_speed_up__3.tsv (X axis @ 5s)

high_pressure_pump_80percent__4.tsv (X axis @ 5s)

compressor_shc2_klima4_bad.tsv (X axis @ 5s)

compressor_shc2_klima5_good.tsv (X axis @ 5s)

compressor_top_1.tsv (X axis @ 5s)

compressor_top_2.tsv (X axis @ 5s)

compressor_top_3.tsv (X axis @ 5s)

compressor_base.tsv (X axis @ 5s)

compressor_side.tsv (X axis @ 5s)

Harmonic series detection in X axis

show_harmonic_series(x_spectra, 'x', T_SEC)

high_pressure_pump_40percent__1.tsv (X axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	20.3906	0.0146296
2	43.0469	0.0164909
3	56.6406	0.0124512
4	79.2969	0.00816218
5	122.344	0.00463894
6	160.859	0.0106926
7	380.625	0.00167143

high_pressure_pump_40percent__2.tsv (X axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	11.3281	0.00480457
2	24.9219	0.00642867
3	31.7188	0.00817352
4	43.0469	0.0144605
5	65.7031	0.0138305
6	77.0312	0.00369309
7	142.734	0.00450612
8	154.062	0.00269428

high_pressure_pump_40percent_speed_up__3.tsv (X axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	18.125	0.00644368
2	52.1094	0.0292742
3	72.5	0.0186523
4	106.484	0.0102005
5	197.109	0.00354446
6	287.734	0.00405812

high_pressure_pump_80percent__4.tsv (X axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	24.9219	0.0209609
2	47.5781	0.40815
3	95.1562	0.684107
4	120.078	0.00876636
5	142.734	0.025571
6	552.812	0.008082

compressor_shc2_klima4_bad.tsv (X axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	154.062	0.0283792
2	308.125	0.010593
3	462.188	0.0145172

compressor_shc2_klima5_good.tsv (X axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	52.1094	0.0646617
2	104.219	0.00945951
3	156.328	0.054688
4	208.438	0.0174424
5	260.547	0.00557364
6	364.766	0.00482011

compressor_top_1.tsv (X axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	47.5781	0.766224
2	145	0.0602588
3	188.047	0.0153765
4	233.359	0.016698
5	471.25	0.0187228

compressor_top_2.tsv (X axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	49.8438	0.825486
2	99.6875	0.0560163
3	149.531	0.0794685
4	199.375	0.0667731
5	292.266	0.0140927
6	489.375	0.0125749
7	539.219	0.0171051

compressor_top_3.tsv (X axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	49.8438	1.00669
2	99.6875	0.0744555
3	149.531	0.0771403
4	199.375	0.0800229
5	294.531	0.059878

compressor_base.tsv (X axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	49.8438	0.921125
2	99.6875	0.0602615
3	149.531	0.0606726
4	199.375	0.0462516
5	292.266	0.00746856

compressor_side.tsv (X axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	49.8438	0.605295
2	99.6875	0.16705
3	149.531	0.122099
4	199.375	0.0740995
5	536.953	0.018745

show_spectra_largest_amplitudes(x_spectra, 'x', T_SEC)

high_pressure_pump_40percent__1.tsv (X axis @ 5s)

• Fundamental frequency: 49.84375 Hz

	f	y	1x
0	49.8438	0.0375268	1
1	6.79688	0.0114317	0.136364
2	36.25	0.00690706	0.727273
3	131.406	0.00515057	2.63636
4	233.359	0.00409289	4.68182

high_pressure_pump_40percent__2.tsv (X axis @ 5s)

• Fundamental frequency: 43.046875 Hz

	f	y	1x
0	43.0469	0.0144605	1
1	24.9219	0.00642867	0.578947
2	11.3281	0.00480457	0.263158
3	380.625	0.00380404	8.84211
4	226.562	0.00309202	5.26316

high_pressure_pump_40percent_speed_up__3.tsv (X axis @ 5s)

• Fundamental frequency: 52.109375 Hz

	f	y	1x
0	52.1094	0.0292742	1
1	27.1875	0.00880891	0.521739
2	457.656	0.00643	8.78261
3	546.016	0.00498029	10.4783
4	337.578	0.00466762	6.47826

high_pressure_pump_80percent__4.tsv (X axis @ 5s)

• Fundamental frequency: 95.15625 Hz

	f	y	1x
0	95.1562	0.684107	1
1	15.8594	0.0483113	0.166667
2	475.781	0.0287978	5
3	396.484	0.0242131	4.16667
4	457.656	0.0197323	4.80952

compressor_shc2_klima4_bad.tsv (X axis @ 5s)

• Fundamental frequency: 360.234375 Hz

	f	y	1x
0	360.234	0.0316232	1
1	29.4531	0.0136152	0.081761
2	514.297	0.00654999	1.42767
3	353.438	0.00428734	0.981132
4	410.078	0.00351766	1.13836

compressor_shc2_klima5_good.tsv (X axis @ 5s)

• Fundamental frequency: 52.109375 Hz

	f	y	1x
0	52.1094	0.0646617	1
1	6.79688	0.00821841	0.130435
2	260.547	0.00557364	5
3	364.766	0.00482011	7
4	65.7031	0.00368113	1.26087

compressor_top_1.tsv (X axis @ 5s)

• Fundamental frequency: 47.578125 Hz

	f	y	1x
0	47.5781	0.766224	1
1	339.844	0.0890469	7.14286
2	145	0.0602588	3.04762
3	346.641	0.027358	7.28571
4	104.219	0.0223045	2.19048

compressor_top_2.tsv (X axis @ 5s)

• Fundamental frequency: 49.84375 Hz

	f	y	1x
0	49.8438	0.825486	1
1	548.281	0.117761	11
2	249.219	0.0457725	5
3	240.156	0.0205001	4.81818
4	323.984	0.0182378	6.5

compressor_top_3.tsv (X axis @ 5s)

• Fundamental frequency: 49.84375 Hz

	f	y	1x
0	49.8438	1.00669	1
1	348.906	0.116427	7
2	249.219	0.0341733	5
3	142.734	0.0277731	2.86364
4	206.172	0.0205308	4.13636

compressor_base.tsv (X axis @ 5s)

• Fundamental frequency: 49.84375 Hz

	f	y	1x
0	49.8438	0.921125	1
1	348.906	0.0496577	7
2	398.75	0.0371128	8
3	410.078	0.0186843	8.22727
4	163.125	0.00976747	3.27273

compressor_side.tsv (X axis @ 5s)

• Fundamental frequency: 49.84375 Hz

	f	y	1x
0	49.8438	0.605295	1
1	346.641	0.157153	6.95455
2	308.125	0.0514137	6.18182
3	536.953	0.018745	10.7727
4	369.297	0.015345	7.40909

Spectrogram in Y axis

y_spectra = get_spectrograms(DATASET, 'y')

high_pressure_pump_40percent__1.tsv (Y axis, Fundamental = 0.0299 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

high_pressure_pump_40percent__2.tsv (Y axis, Fundamental = 33.1799 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

high_pressure_pump_40percent_speed_up__3.tsv (Y axis, Fundamental = 0.0306 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

high_pressure_pump_80percent__4.tsv (Y axis, Fundamental = 0.0625 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_shc2_klima4_bad.tsv (Y axis, Fundamental = 50.9893 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_shc2_klima5_good.tsv (Y axis, Fundamental = 50.4216 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_top_1.tsv (Y axis, Fundamental = 47.9129 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_top_2.tsv (Y axis, Fundamental = 49.4398 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_top_3.tsv (Y axis, Fundamental = 48.6810 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_base.tsv (Y axis, Fundamental = 48.8258 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_side.tsv (Y axis, Fundamental = 49.6205 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

Spectrogram detail in Y axis

show_spectrogram_detail(y_spectra, 'y', T_SEC)

high_pressure_pump_40percent__1.tsv (Y axis @ 5s)

high_pressure_pump_40percent__2.tsv (Y axis @ 5s)

high_pressure_pump_40percent_speed_up__3.tsv (Y axis @ 5s)

high_pressure_pump_80percent__4.tsv (Y axis @ 5s)

compressor_shc2_klima4_bad.tsv (Y axis @ 5s)

compressor_shc2_klima5_good.tsv (Y axis @ 5s)

compressor_top_1.tsv (Y axis @ 5s)

compressor_top_2.tsv (Y axis @ 5s)

compressor_top_3.tsv (Y axis @ 5s)

compressor_base.tsv (Y axis @ 5s)

compressor_side.tsv (Y axis @ 5s)

Peaks in frequency spectrum in Y axis

show_mms_peaks(y_spectra, 'y', T_SEC)

high_pressure_pump_40percent__1.tsv (Y axis @ 5s)

high_pressure_pump_40percent__2.tsv (Y axis @ 5s)

high_pressure_pump_40percent_speed_up__3.tsv (Y axis @ 5s)

high_pressure_pump_80percent__4.tsv (Y axis @ 5s)

compressor_shc2_klima4_bad.tsv (Y axis @ 5s)

compressor_shc2_klima5_good.tsv (Y axis @ 5s)

compressor_top_1.tsv (Y axis @ 5s)

compressor_top_2.tsv (Y axis @ 5s)

compressor_top_3.tsv (Y axis @ 5s)

compressor_base.tsv (Y axis @ 5s)

compressor_side.tsv (Y axis @ 5s)

Harmonic series detection in Y axis

show_harmonic_series(y_spectra, 'y', T_SEC)

high_pressure_pump_40percent__1.tsv (Y axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	20.3906	0.0146296
2	43.0469	0.0164909
3	56.6406	0.0124512
4	79.2969	0.00816218
5	122.344	0.00463894
6	160.859	0.0106926
7	380.625	0.00167143

high_pressure_pump_40percent__2.tsv (Y axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	11.3281	0.00480457
2	24.9219	0.00642867
3	31.7188	0.00817352
4	43.0469	0.0144605
5	65.7031	0.0138305
6	77.0312	0.00369309
7	142.734	0.00450612
8	154.062	0.00269428

high_pressure_pump_40percent_speed_up__3.tsv (Y axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	18.125	0.00644368
2	52.1094	0.0292742
3	72.5	0.0186523
4	106.484	0.0102005
5	197.109	0.00354446
6	287.734	0.00405812

high_pressure_pump_80percent__4.tsv (Y axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	24.9219	0.0209609
2	47.5781	0.40815
3	95.1562	0.684107
4	120.078	0.00876636
5	142.734	0.025571
6	552.812	0.008082

compressor_shc2_klima4_bad.tsv (Y axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	154.062	0.0283792
2	308.125	0.010593
3	462.188	0.0145172

compressor_shc2_klima5_good.tsv (Y axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	52.1094	0.0646617
2	104.219	0.00945951
3	156.328	0.054688
4	208.438	0.0174424
5	260.547	0.00557364
6	364.766	0.00482011

compressor_top_1.tsv (Y axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	47.5781	0.766224
2	145	0.0602588
3	188.047	0.0153765
4	233.359	0.016698
5	471.25	0.0187228

compressor_top_2.tsv (Y axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	49.8438	0.825486
2	99.6875	0.0560163
3	149.531	0.0794685
4	199.375	0.0667731
5	292.266	0.0140927
6	489.375	0.0125749
7	539.219	0.0171051

compressor_top_3.tsv (Y axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	49.8438	1.00669
2	99.6875	0.0744555
3	149.531	0.0771403
4	199.375	0.0800229
5	294.531	0.059878

compressor_base.tsv (Y axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	49.8438	0.921125
2	99.6875	0.0602615
3	149.531	0.0606726
4	199.375	0.0462516
5	292.266	0.00746856

compressor_side.tsv (Y axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	49.8438	0.605295
2	99.6875	0.16705
3	149.531	0.122099
4	199.375	0.0740995
5	536.953	0.018745

show_spectra_largest_amplitudes(y_spectra, 'y', T_SEC)

high_pressure_pump_40percent__1.tsv (Y axis @ 5s)

• Fundamental frequency: 49.84375 Hz

	f	y	1x
0	49.8438	0.0375268	1
1	6.79688	0.0114317	0.136364
2	36.25	0.00690706	0.727273
3	131.406	0.00515057	2.63636
4	233.359	0.00409289	4.68182

high_pressure_pump_40percent__2.tsv (Y axis @ 5s)

• Fundamental frequency: 43.046875 Hz

	f	y	1x
0	43.0469	0.0144605	1
1	24.9219	0.00642867	0.578947
2	11.3281	0.00480457	0.263158
3	380.625	0.00380404	8.84211
4	226.562	0.00309202	5.26316

high_pressure_pump_40percent_speed_up__3.tsv (Y axis @ 5s)

• Fundamental frequency: 52.109375 Hz

	f	y	1x
0	52.1094	0.0292742	1
1	27.1875	0.00880891	0.521739
2	457.656	0.00643	8.78261
3	546.016	0.00498029	10.4783
4	337.578	0.00466762	6.47826

high_pressure_pump_80percent__4.tsv (Y axis @ 5s)

• Fundamental frequency: 95.15625 Hz

	f	y	1x
0	95.1562	0.684107	1
1	15.8594	0.0483113	0.166667
2	475.781	0.0287978	5
3	396.484	0.0242131	4.16667
4	457.656	0.0197323	4.80952

compressor_shc2_klima4_bad.tsv (Y axis @ 5s)

• Fundamental frequency: 360.234375 Hz

	f	y	1x
0	360.234	0.0316232	1
1	29.4531	0.0136152	0.081761
2	514.297	0.00654999	1.42767
3	353.438	0.00428734	0.981132
4	410.078	0.00351766	1.13836

compressor_shc2_klima5_good.tsv (Y axis @ 5s)

• Fundamental frequency: 52.109375 Hz

	f	y	1x
0	52.1094	0.0646617	1
1	6.79688	0.00821841	0.130435
2	260.547	0.00557364	5
3	364.766	0.00482011	7
4	65.7031	0.00368113	1.26087

compressor_top_1.tsv (Y axis @ 5s)

• Fundamental frequency: 47.578125 Hz

	f	y	1x
0	47.5781	0.766224	1
1	339.844	0.0890469	7.14286
2	145	0.0602588	3.04762
3	346.641	0.027358	7.28571
4	104.219	0.0223045	2.19048

compressor_top_2.tsv (Y axis @ 5s)

• Fundamental frequency: 49.84375 Hz

	f	y	1x
0	49.8438	0.825486	1
1	548.281	0.117761	11
2	249.219	0.0457725	5
3	240.156	0.0205001	4.81818
4	323.984	0.0182378	6.5

compressor_top_3.tsv (Y axis @ 5s)

• Fundamental frequency: 49.84375 Hz

	f	y	1x
0	49.8438	1.00669	1
1	348.906	0.116427	7
2	249.219	0.0341733	5
3	142.734	0.0277731	2.86364
4	206.172	0.0205308	4.13636

compressor_base.tsv (Y axis @ 5s)

• Fundamental frequency: 49.84375 Hz

	f	y	1x
0	49.8438	0.921125	1
1	348.906	0.0496577	7
2	398.75	0.0371128	8
3	410.078	0.0186843	8.22727
4	163.125	0.00976747	3.27273

compressor_side.tsv (Y axis @ 5s)

• Fundamental frequency: 49.84375 Hz

	f	y	1x
0	49.8438	0.605295	1
1	346.641	0.157153	6.95455
2	308.125	0.0514137	6.18182
3	536.953	0.018745	10.7727
4	369.297	0.015345	7.40909

Spectrogram in Z axis

z_spectra = get_spectrograms(DATASET, 'z')

high_pressure_pump_40percent__1.tsv (Z axis, Fundamental = 0.0299 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

high_pressure_pump_40percent__2.tsv (Z axis, Fundamental = 25.3960 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

high_pressure_pump_40percent_speed_up__3.tsv (Z axis, Fundamental = 47.8300 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

high_pressure_pump_80percent__4.tsv (Z axis, Fundamental = 47.5881 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_shc2_klima4_bad.tsv (Z axis, Fundamental = 50.2110 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_shc2_klima5_good.tsv (Z axis, Fundamental = 50.4890 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_top_1.tsv (Z axis, Fundamental = 0.0551 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_top_2.tsv (Z axis, Fundamental = 49.4398 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_top_3.tsv (Z axis, Fundamental = 48.6810 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_base.tsv (Z axis, Fundamental = 48.8258 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

compressor_side.tsv (Z axis, Fundamental = 49.6205 Hz)

Window size: 512
Heinsenberg box
	Time step: 441.37931034482756 ms
	Frequency step: 2.265625 Hz

Spectrogram detail in Z axis

show_spectrogram_detail(z_spectra, 'z', T_SEC)

high_pressure_pump_40percent__1.tsv (Z axis @ 5s)

high_pressure_pump_40percent__2.tsv (Z axis @ 5s)

high_pressure_pump_40percent_speed_up__3.tsv (Z axis @ 5s)

high_pressure_pump_80percent__4.tsv (Z axis @ 5s)

compressor_shc2_klima4_bad.tsv (Z axis @ 5s)

compressor_shc2_klima5_good.tsv (Z axis @ 5s)

compressor_top_1.tsv (Z axis @ 5s)

compressor_top_2.tsv (Z axis @ 5s)

compressor_top_3.tsv (Z axis @ 5s)

compressor_base.tsv (Z axis @ 5s)

compressor_side.tsv (Z axis @ 5s)

Peaks in frequency spectrum in Z axis

show_mms_peaks(z_spectra, 'z', T_SEC)

high_pressure_pump_40percent__1.tsv (Z axis @ 5s)

high_pressure_pump_40percent__2.tsv (Z axis @ 5s)

high_pressure_pump_40percent_speed_up__3.tsv (Z axis @ 5s)

high_pressure_pump_80percent__4.tsv (Z axis @ 5s)

compressor_shc2_klima4_bad.tsv (Z axis @ 5s)

compressor_shc2_klima5_good.tsv (Z axis @ 5s)

compressor_top_1.tsv (Z axis @ 5s)

compressor_top_2.tsv (Z axis @ 5s)

compressor_top_3.tsv (Z axis @ 5s)

compressor_base.tsv (Z axis @ 5s)

compressor_side.tsv (Z axis @ 5s)

Harmonic series detection in Z axis

show_harmonic_series(z_spectra, 'z', T_SEC)

high_pressure_pump_40percent__1.tsv (Z axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	20.3906	0.0146296
2	43.0469	0.0164909
3	56.6406	0.0124512
4	79.2969	0.00816218
5	122.344	0.00463894
6	160.859	0.0106926
7	380.625	0.00167143

high_pressure_pump_40percent__2.tsv (Z axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	11.3281	0.00480457
2	24.9219	0.00642867
3	31.7188	0.00817352
4	43.0469	0.0144605
5	65.7031	0.0138305
6	77.0312	0.00369309
7	142.734	0.00450612
8	154.062	0.00269428

high_pressure_pump_40percent_speed_up__3.tsv (Z axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	18.125	0.00644368
2	52.1094	0.0292742
3	72.5	0.0186523
4	106.484	0.0102005
5	197.109	0.00354446
6	287.734	0.00405812

high_pressure_pump_80percent__4.tsv (Z axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	24.9219	0.0209609
2	47.5781	0.40815
3	95.1562	0.684107
4	120.078	0.00876636
5	142.734	0.025571
6	552.812	0.008082

compressor_shc2_klima4_bad.tsv (Z axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	154.062	0.0283792
2	308.125	0.010593
3	462.188	0.0145172

compressor_shc2_klima5_good.tsv (Z axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	52.1094	0.0646617
2	104.219	0.00945951
3	156.328	0.054688
4	208.438	0.0174424
5	260.547	0.00557364
6	364.766	0.00482011

compressor_top_1.tsv (Z axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	47.5781	0.766224
2	145	0.0602588
3	188.047	0.0153765
4	233.359	0.016698
5	471.25	0.0187228

compressor_top_2.tsv (Z axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	49.8438	0.825486
2	99.6875	0.0560163
3	149.531	0.0794685
4	199.375	0.0667731
5	292.266	0.0140927
6	489.375	0.0125749
7	539.219	0.0171051

compressor_top_3.tsv (Z axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	49.8438	1.00669
2	99.6875	0.0744555
3	149.531	0.0771403
4	199.375	0.0800229
5	294.531	0.059878

compressor_base.tsv (Z axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	49.8438	0.921125
2	99.6875	0.0602615
3	149.531	0.0606726
4	199.375	0.0462516
5	292.266	0.00746856

compressor_side.tsv (Z axis @ 5s)

	Frequency [Hz]	Amplitude [m/s^2]
1	49.8438	0.605295
2	99.6875	0.16705
3	149.531	0.122099
4	199.375	0.0740995
5	536.953	0.018745

show_spectra_largest_amplitudes(z_spectra, 'z', T_SEC)

high_pressure_pump_40percent__1.tsv (Z axis @ 5s)

• Fundamental frequency: 49.84375 Hz

	f	y	1x
0	49.8438	0.0375268	1
1	6.79688	0.0114317	0.136364
2	36.25	0.00690706	0.727273
3	131.406	0.00515057	2.63636
4	233.359	0.00409289	4.68182

high_pressure_pump_40percent__2.tsv (Z axis @ 5s)

• Fundamental frequency: 43.046875 Hz

	f	y	1x
0	43.0469	0.0144605	1
1	24.9219	0.00642867	0.578947
2	11.3281	0.00480457	0.263158
3	380.625	0.00380404	8.84211
4	226.562	0.00309202	5.26316

high_pressure_pump_40percent_speed_up__3.tsv (Z axis @ 5s)

• Fundamental frequency: 52.109375 Hz

	f	y	1x
0	52.1094	0.0292742	1
1	27.1875	0.00880891	0.521739
2	457.656	0.00643	8.78261
3	546.016	0.00498029	10.4783
4	337.578	0.00466762	6.47826

high_pressure_pump_80percent__4.tsv (Z axis @ 5s)

• Fundamental frequency: 95.15625 Hz

	f	y	1x
0	95.1562	0.684107	1
1	15.8594	0.0483113	0.166667
2	475.781	0.0287978	5
3	396.484	0.0242131	4.16667
4	457.656	0.0197323	4.80952

compressor_shc2_klima4_bad.tsv (Z axis @ 5s)

• Fundamental frequency: 360.234375 Hz

	f	y	1x
0	360.234	0.0316232	1
1	29.4531	0.0136152	0.081761
2	514.297	0.00654999	1.42767
3	353.438	0.00428734	0.981132
4	410.078	0.00351766	1.13836

compressor_shc2_klima5_good.tsv (Z axis @ 5s)

• Fundamental frequency: 52.109375 Hz

	f	y	1x
0	52.1094	0.0646617	1
1	6.79688	0.00821841	0.130435
2	260.547	0.00557364	5
3	364.766	0.00482011	7
4	65.7031	0.00368113	1.26087

compressor_top_1.tsv (Z axis @ 5s)

• Fundamental frequency: 47.578125 Hz

	f	y	1x
0	47.5781	0.766224	1
1	339.844	0.0890469	7.14286
2	145	0.0602588	3.04762
3	346.641	0.027358	7.28571
4	104.219	0.0223045	2.19048

compressor_top_2.tsv (Z axis @ 5s)

• Fundamental frequency: 49.84375 Hz

	f	y	1x
0	49.8438	0.825486	1
1	548.281	0.117761	11
2	249.219	0.0457725	5
3	240.156	0.0205001	4.81818
4	323.984	0.0182378	6.5

compressor_top_3.tsv (Z axis @ 5s)

• Fundamental frequency: 49.84375 Hz

	f	y	1x
0	49.8438	1.00669	1
1	348.906	0.116427	7
2	249.219	0.0341733	5
3	142.734	0.0277731	2.86364
4	206.172	0.0205308	4.13636

compressor_base.tsv (Z axis @ 5s)

• Fundamental frequency: 49.84375 Hz

	f	y	1x
0	49.8438	0.921125	1
1	348.906	0.0496577	7
2	398.75	0.0371128	8
3	410.078	0.0186843	8.22727
4	163.125	0.00976747	3.27273

compressor_side.tsv (Z axis @ 5s)

• Fundamental frequency: 49.84375 Hz

	f	y	1x
0	49.8438	0.605295	1
1	346.641	0.157153	6.95455
2	308.125	0.0514137	6.18182
3	536.953	0.018745	10.7727
4	369.297	0.015345	7.40909

Histogram

axis = ['x', 'y', 'z']
for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    ts[axis].hist(figsize=(10, 5), grid=True, bins=50)
    plt.show()

high_pressure_pump_40percent__1.tsv

high_pressure_pump_40percent__2.tsv

high_pressure_pump_40percent_speed_up__3.tsv

high_pressure_pump_80percent__4.tsv

compressor_shc2_klima4_bad.tsv

compressor_shc2_klima5_good.tsv

compressor_top_1.tsv

compressor_top_2.tsv

compressor_top_3.tsv

compressor_base.tsv

compressor_side.tsv

Orbitals of all cross sections

for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    fig, ax = plt.subplots(1, 3, figsize=(20, 4))

    for i, col in enumerate([('x', 'y'), ('x', 'z'), ('y', 'z')]):
        ax[i].scatter(ts[col[0]], ts[col[1]], s=1)
        ax[i].grid(True)
        ax[i].set_xlabel(col[0].upper())
        ax[i].set_ylabel(col[1].upper())
        ax[i].grid(True)
    plt.show()       # plt.savefig('orbitals.png')

high_pressure_pump_40percent__1.tsv

high_pressure_pump_40percent__2.tsv

high_pressure_pump_40percent_speed_up__3.tsv

high_pressure_pump_80percent__4.tsv

compressor_shc2_klima4_bad.tsv

compressor_shc2_klima5_good.tsv

compressor_top_1.tsv

compressor_top_2.tsv

compressor_top_3.tsv

compressor_base.tsv

compressor_side.tsv

Orbitals of 1x harmonic frequency

x_spectra_by_name = {spec[0]: spec for spec in x_spectra}
y_spectra_by_name = {spec[0]: spec for spec in y_spectra}
z_spectra_by_name = {spec[0]: spec for spec in z_spectra}
t = 5
space = 5

for name, ts in DATASET:
    display(Markdown(f'**{name}**'))
    fig, ax = plt.subplots(1, 3, figsize=(20, 4))

    name, freqs, Pxx = x_spectra_by_name[name]
    x_fundamental = get_max_frequency(freqs, Pxx, window_idx(t))

    name, freqs, Pxx = y_spectra_by_name[name]
    y_fundamental = get_max_frequency(freqs, Pxx, window_idx(t))

    name, freqs, Pxx = z_spectra_by_name[name]
    z_fundamental = get_max_frequency(freqs, Pxx, window_idx(t))

    ts['x_1x'] = butter_bandpass_filter(ts['x'], x_fundamental - space, x_fundamental + space, Fs)
    ts['y_1x'] = butter_bandpass_filter(ts['y'], y_fundamental - space, y_fundamental + space, Fs)
    ts['z_1x'] = butter_bandpass_filter(ts['z'], z_fundamental - space, z_fundamental + space, Fs)
    
    for i, col in enumerate([('x_1x', 'y_1x'), ('x_1x', 'z_1x'), ('y_1x', 'z_1x')]):
        ax[i].scatter(ts[col[0]], ts[col[1]], s=1)
        ax[i].grid(True)
        ax[i].set_xlabel(col[0].upper())
        ax[i].set_ylabel(col[1].upper())
        ax[i].grid(True)
    
    plt.show()       # plt.savefig('orbitals_1x.png')

high_pressure_pump_40percent__1.tsv

high_pressure_pump_40percent__2.tsv

high_pressure_pump_40percent_speed_up__3.tsv

high_pressure_pump_80percent__4.tsv

compressor_shc2_klima4_bad.tsv

compressor_shc2_klima5_good.tsv

compressor_top_1.tsv

compressor_top_2.tsv

compressor_top_3.tsv

compressor_base.tsv

compressor_side.tsv